The gas/accelator/throttle pedal opens the throttle (a spring closes it). The throttle is a flap in the passageway of air going into the engine for combustion. Thus your accelerator control is directly controlling how much air can be drawn into the engine’s cylinders. The fuel system – carburetor or fuel injection – is designed to provide a proportionate amount of fuel so the engine will have air and fuel together to burn.
Fuel must be vaporized to burn efficiently, and cold engines don’t vaporize it as well as warm engines, so there is some system to add some extra fuel for starting and running a cold engine. While a smaller percentage of it is vaporized, with the greater total amount of fuel the result is that about the same amount of vaporized fuel is available.
Most carburetors, and a tiny handful of older fuel injection systems, used a choke to add extra fuel when cold. A choke is a flap like the throttle, located in the air passageway where its restriction of airflow doesn’t cause a proportionate lessening of fuel delivered, thus having the overall effect of increasing the amount of fuel going into the engine. Note that throttle and choke are related terms, and have the same meaning when talking about restricting airflow through a person’s throat. In automotive use, the terms are used quite specifically for their different respective functions, even though their mechanisms are essentially identical.
Now, with that background: Older carbureted cars needed to idle at a significantly higher speed while cold, in order to deal with the extra gas provided by the choke. So along with the choke there’s a fast idle mechanism. It has either a series of steps or a ramped design. to provide the greatest idle increase with the choke full on, and progressively less increase as the choke is working its way to the off position during warmup.
The choke pulls the fast idle cam along with it when going on (cold engine). But while the choke spring would automatically try to do this as the engine got cold, the full motion would be blocked by the fast idle cam hitting the idle screw, which would be left in its normal warm idle position. So, you floor the gas pedal on the cold engine and voila: A) the fast idle cam can move into its cold position, B) the choke moves to its on position, and C) the accelerator pump gives a priming squirt of gas. Turn the key, and the engine starts and runs at fast idle.
The choke gradually goes to its off postion as the car warms up. However, the fast idle cam will stay where it was until the gas pedal is opened, because the idle screw is pressed against it. If you blip the pedal every minute during warmup, the fast idle comes down gradually. If you leave it alone for several minutes, it comes down in a bigger jump. Tapping on the pedal releases the pressure of the idle screw on the fast idle cam, and lets the cam go to where it “wants” to be.
On modern fuel injected cars, the same things are accomplished in very different ways. Fuel mixture (e.g., extra gas for starting cold) and idle speed are controlled by the electronic control system (computer). There’s no need to step on the gas pedal to activate it for a cold start, because there’s no mechanism that has to move into position. The idle speed is higher when cold, but not as much higher as with carbureted cars, because fuel injection systems can very effectively do “just enough” of everything. The transition from fast idle to warm idle is gradual and smooth without noticeable jumps.